Conference article

PDEModelica and Breathing in an Avalanche

Jan Šilar
Institute of Pathological physiology, First Faculty of Medicine, Charles University, Prague, Czech republic

Filip Ježek
Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic

Jirí Kofránek
Institute of Pathological physiology, First Faculty of Medicine, Charles University, Prague, Czech republic

Download articlehttp://dx.doi.org/10.3384/ecp17132367

Published in: Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017

Linköping Electronic Conference Proceedings 132:41, p. 367-372

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Published: 2017-07-04

ISBN: 978-91-7685-575-1

ISSN: 1650-3686 (print), 1650-3740 (online)

Abstract

This paper presents a Modelica language extension for partial differential equations (PDE) called PDEModelica. Support for this extension is implemented in OpenModelica. This support is limited to 1-dimensional problems and the first and second partial derivatives. PDEModelica is introduced by a string equation model and later by a real life model of respiration during a snow burial. This model describes CO2 advection and diffusion in snow described by advection-diffusion PDE.

Keywords

PDEModelica, PDE, avalanche survival

References

Courant, R., Friedrichs, K., Lewy, H., 1967. On the Partial Difference Equations of Mathematical Physics. IBM J. Res. Dev. 11, 215–234.

Dshabarow, F., Cellier, F.E., Zimmer, D., Dshabarow, F., Com, C., Ch, I.E., 2007. Support for Dymola in the modeling and simulation of physical systems with distributed parameters. In: Proceedings of the 6th International Modelica Conference. pp. 683–690.

Fritzson, P., 2015. Principles of Object-Oriented Modeling and Simulation with Modelica 3.3: A Cyber-Physical Approach. John Wiley & Sons.

Margid, J., Beidleman, N., Harmston, C., 1998. O2 and CO2 levels with the Black Diamond AvaLung during human snow burials lasting up to one hour. Proceedings of the.

Mateják, M., Kofránek, J., 2015. Physiomodel - an integrative physiology in Modelica. In: 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). ieeexplore.ieee.org, pp. 1464–1467.

McIntosh, S.E., Grissom, C.K., Olivares, C.R., Kim, H.S., Tremper, B., 2007. Cause of death in avalanche fatalities. Wilderness Environ. Med. 18, 293–297.

Radwin, M.I., Grissom, C.K., Scholand, M.B., Harmston, C.H., 2001. Normal oxygenation and ventilation during snow burial by the exclusion of exhaled carbon dioxide. Wilderness Environ. Med. 12, 256–262.

Roubík, K., Sieger, L., Sykora, K., 2015. Work of Breathing into Snow in the Presence versus Absence of an Artificial Air Pocket Affects Hypoxia and Hypercapnia of a Victim Covered with Avalanche Snow: A Randomized Double Blind Crossover Study. PLoS One 10, e0144332.

Saldamli, L., 2006. PDEModelica A High-Level Language for Modeling with Partial Differential Equations (PhD Thesis.). Linkopings universitet.

Schiesser, W.E., 2012. The Numerical Method of Lines: Integration of Partial Differential Equations. Elsevier.

Stavåker, K., Fritzson, P. et al, 2014. PDE Modeling With Modelica Via FMI Import Of Hiflow3 C++ Components With Parallel Multi-core Simulations. Proceedings of the 55th Scandinavian Conference on Simulation and Modeling.

Strikwerda, J.C., 2004. Finite Difference Schemes and Partial Differential Equations. SIAM.

Techel, F., Jarry, F., Kronthaler, G., Mitterer, S., Nairz, P., Pavšek, M., Valt, M., Darms, G., 2016. Avalanche fatalities in the European Alps: long-term trends and statistics. Geogr. Helv. 71, 147–159.

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